DERIVE for Windows version 5.04 DfW file saved on 13 Dec 2004  ITERATION(i):=[443576/1241109] ITERATION2(i):=ITERATES(x^(-x) + x, x, , i) L(i):=ITERATE(x^(-x), x, , i) LIMITE(n):=ITERATE(u(a), a, 0, n) f(x):=x^(-x) g(x):=f'(x) u(n):=IF(n = 0, , ^(- u(n - 1))u(n - 1)) w(n):=LN(u(n)) a:=x = 377123/1055176 hCross:=APPROX(6444007858545927/20000000000000000) m:=1/4 vCross:=APPROX(4807330827067669/2500000000000000) :=893507339/2500000000 3CExpnObj8  Utilisateurf(x):=x*EXP(-x)8$< Lim(#1,x)LIM(f(x):=x*EXP(-x),x,+inf,0)HTSimp(Lim(#1,x))08`Xl Utilisateurf(x)8xp Utilisateur DIF(f(x),x)8 Approx(#5) #e^(-x)*(1-x)8 Utilisateurg(x):=DIF(f(x),x)8x Utilisateurg(x)=08  Resol(#8,x) SOLVE(g(x)=0,x,Real),@8Simp(Resol(#8,x))Mb?  x=inf OR x=18DxP Utilisateur g(x)>08\h Resol(#11,x) SOLVE(g(x)>0,x,Real)t Simp(Resol(#11,x)) x<18X Utilisateurf(1)8X Utilisateurf(1)8 Approx(#15) 0.36787944118X Utilisateurf(1) Simp(#17)#e^(-1)8X Utilisateurf(x)( @Simp(Utilisateur) x*#e^(-x)8LXX Utilisateurf(x)d | Approx(#21) x*#e^(-x) Approx(Utilisateur) x*#e^(-x)8X Utilisateurf(x)  Approx(#24) x*#e^(-x) CDispOleObjlP CDispItemࡱ>  O !"#$%&'()*+,-./0123456789:;<=>?@ABCDEFGHIJKLMNOPQRSTUVWXYZ[\]^_`abcdefghijklmnopqrstuvwxyz{|}~Root EntryF WWOle CONTENTSbuCompObjr F,Image (bitmap indpendante du priphrique) StaticDib9q      !"#$%&'()*+,-./0123456789:;<=>?@ABCDEFGHIJKLMNOPQRSTUVWXYZ[\]^_`abcdefghijklmnopqrstuvwxyz{|}~      !"#$%&'()*+,-./0123456789:;<=>?@ABCDEFGHIJKLMNOPQRSTUVWXYZ[\]^_`abcdefghijklmnopqrstuvwxyz{|}~      !"#$%&'()*+,-./0123456789:;<=>?@ABCDEFGHIJKLMNOPQRSTUVWXYZ[\]^_`abcdefghijklmnopqrstuvwxyz{|}~      !"#$%&'()*+,-./0123456789:;<=>?@ABCDEFGHIJKLMNOPQRSTUVWXYZ[\]^_`abcdefghijklmnopqrstuvwxyz{|}~      !"#$%&'()*+,-./0123456789:;<=>?@ABCDEFGHIJKLMNOPQRSTUVWXYZ[\]^_`abcdefghijklmnopqrstuvwxyz{|}~      !"#$%&'()*+,-./0123456789:;<=>?@ABCDEFGHIJKLMNOPQRSTUVWXYZ[\]^_`abcdefghijklmnopqrstuvwxyz{|}~      !"#$%&'()*+,-./0123456789:;<=>?@ABCDEFGHIJKLMNOPQRSTUVWXYZ[\]^_`abcdefghijklmnopqrstuvwxyz{|}~      !"#$%&'()*+,-./0123456789:;<=>?@ABCDEFGHIJKLMNBMbuB(h  uCONTENTS8\ Utilisateurf(x)=1/48 Resol(#26,x)NSOLVE(f(x)=1/4,x,Real)HSimp(Resol(#26,x))Q?x=0.35740293568 Utilisateurf(x)=1/480( Resol(#29,x)NSOLVE(f(x)=1/4,x,0.36,10)4@@Simp(Resol(#29,x))Mb? x=2.153292438LxX Utilisateur f(x)=08dp Resol(#32,x)!NSOLVE(f(x)=0,x,Real)| Simp(Resol(#32,x))"x=08 Utilisateur# f(x)=1/#e8 Resol(#35,x)$NSOLVE(f(x)=1/#e,x,Real)HSimp(Resol(#35,x))Mb?%x=0.99999904638  Utilisateur&alpha:=0.35740293568$ T Utilisateur''u(n):=IF(n=0,alpha,u(n-1)*EXP(-u(n-1)))8`l Utilisateur(+ITERATION(i):=ITERATES(x*EXP(-x),x,alpha,i)8x Utilisateur) ITERATION(3)H Approx(#41)*-[0.3574029356,0.25,0.1947001957,0.1602541066]8 Utilisateur+ ITERATION(15)8 Approx(#43),[0.3574029356,0.25,0.1947001957,0.1602541066,0.1365248453,0.1191021787,0.1057290396,0.09512107479,0.08649005851,0.07932389587,0.07327470952,0.06809752119,0.06361461832,0.05969383050,0.05623474717,0.05315967369]8  Utilisateur-ITERATION(100)8, Approx(#45)Mb?.}[0.3574029356,0.25,0.1947001957,0.1602541066,0.1365248453,0.1191021787,0.1057290396,0.09512107479,0.08649005851,0.07932389587,0.07327470952,0.06809752119,0.06361461832,0.05969383050,0.05623474717,0.05315967369,0.05040752260,0.04792958235,0.04568652136,0.04364622502,0.04178220665,0.04007242187,0.03849837151,0.03704441398,0.03569723221,0.03444541594,0.03327913115,0.03218985617,0.03117016917,0.03021357576,0.02931436814,0.02846750917,0.02766853643,0.02691348231,0.02619880712,0.02552134275,0.02487824508,0.02426695346,0.02368515621,0.02313076097,0.02260186928,0.02209675456,0.02161384303,0.02115169719,0.02070900128,0.02028454871,0.01987723089,0.01948602748,0.01910999778,0.01874827305,0.01840004980,0.01806458373,0.01774118437,0.01742921033,0.01712806494,0.01683719248,0.01655607469,0.01628422765,0.01602119900,0.01576656540,0.01551993022,0.01528092148,0.01504918996,0.01482440749,0.01460626534,0.01439447286,0.01418875616,0.01398885687,0.01379453112,0.01360554849,0.01342169112,0.01324275284,0.01306853842,0.01289886285,0.01273355064,0.01257243530,0.01241535865,0.01226217043,0.01211272773,0.01196689456,0.01182454145,0.01168554508,0.01154978785,0.01141715765,0.01128754746,0.01116085510,0.01103698296,0.01091583774,0.01079733021,0.01068137500,0.01056789039,0.01045679812,0.01034802320,0.01024149375,0.01013714084,0.01003489831,0.009934702699,0.009836493031,0.009740210752,0.009645799585,0.009553205426]8 Utilisateur/w(n):=LN(u(n))8X Utilisateur0u(n)8x Somme(#48,n)1SUM(u(n),n,0,10) 8 Approx(Somme(#48,n))V-?2 1.6579230403